A man leaves the Mosaic Church food bank in Coventry after being given emergency supplies. Photograph: Christopher Thomond for the Guardian

An hour after the Hope Centre food bank opens up for the Tuesday afternoon distribution session, a volunteer apologetically tapes an A4 sheet to the glass doors, announcing "Sorry No Food". Plastic bags full of tinned food and supermarket donations of produce approaching its sell-by date are being distributed to feed 79 people and there is very little left on the shelves in a storeroom of this church in central Coventry.

"We've been back to the warehouse, but we're still struggling," says Karen Sumner, one of the food bank volunteers. "We should be open for two hours but we usually run out of food after an hour."

A man arrives in the rain, very distressed to see the No Food sign. This afternoon he has walked three miles from his home to collect a food parcel, arriving just after the session began, but because he had no ID on him, he then had to walk a mile into the centre of town to get a letter from a charity certifying that he is who he claims to be, and then walk a mile back to be issued with some food. His benefits have been stopped for reasons that are not clear to him, and he faces the prospect of a three-mile walk home again, with no food and no money, until volunteers agree to let him join the crowd of 30 people still waiting in the church's cafe, and promise to find him something to take away.

"There's nothing at home. If I don't get this food I'll end up shoplifting," he says. A sign on the wall, written in chalk on a menu blackboard, advises him: "Psalm 25 vs 8: the Lord is good and does what is right."

A large crowd in the Hope Centre are from Romania, and say they are waiting for food because collecting scrap metal and washing cars isn't enough to make ends meet. A bigger number is there because of benefit delays and cuts, or simply because they are no longer able to make their low wages stretch.

A local supermarket has delivered a load of stock just about to reach its sell-by date (it doesn't want to be named, to avoid getting caught up in discussion of the merits of giving food that is about to go off to the hungry) and today it is offloading industrial quantities of iced buns, which several families take home by the dozen.

The boom in Britain's food banks reflects a number of worrying and complicated trends. As well as rising unemployment, more people are seeing their hours cut at work. For the past couple of years, charities have been warning that a shift to a less generous way of uprating benefits in line with inflation, combined with rising food and fuel prices, would make life more difficult for people claiming benefits. Then there is the start of a new, harsher benefits regime, as a result of which it seems that more claimants are having their payments sanctioned – cut or stopped entirely – if they miss appointments. At the same time, the state system of a social fund and crisis loans is being wound down, so emergency cash payments from the welfare system for those deemed to be in extreme need are now exceptionally difficult to procure. Around 43% of visitors to Trussell Trust distribution centres nationwide come because of changes to their benefits or a crisis loan being refused.

For others, the growth is a reflection of a new approach to providing assistance to people in real need. Whereas previously this was a service that the state would have provided, now feeding large numbers of people who are not able to feed themselves is being subcontracted out to charities. Those who have scrutinised the progress of the Welfare Reform Act, say this move from state to charity reflects the general direction of travel.

Once these services move beyond the realms of state provision, there are potential problems – they lose neutrality, some uncertainty comes with initiatives that are volunteer-run, the food on offer is (despite the best efforts of the Trussell Trust) idiosyncratic, the religious environment in which food is provided raises questions for some recipients. It becomes charity rather than basic state support, and for many this brings a degree of unease.

Stephen Timms, shadow work and pensions secretary, says it is a "pretty worrying reflection of what's going on in the country, when people are dependent on these charitable handouts. My worry is that we are really just at the start of cutting back the benefits system and already a large number of people are not able to buy food for their families. This shouldn't be happening on the scale that it is now happening."

Manchester Labour MP, and former head of the Child Poverty Action Group, Kate Green describes the growth of food banks as a disgrace. "I feel a real burning anger about them," she says. "People are very distressed at having to ask for food; it's humiliating and distressing."

At an earlier distribution session at the Queen's Road Baptist Church, on the ring road near Coventry Station, Paul and Sarah (not their real names) arrive to see if they can get help feeding their family, and look very worried when the volunteer at the church's reception scans a printed list, kept updated by a team of volunteers across the city, which indicates that they have already had three food parcels this year and that they can't have another. Trussell Trust food banks only help people in acute situations, and the organisation doesn't want to encourage people to rely on them, so staff are vigilant about the number of packages they hand out to individuals.

Paul, 33, hasn't had a job since a car accident three years ago damaged his knee and made it hard for him to stand for long stretches; he has now mostly recovered and is looking to return to warehouse work, although he hasn't managed to find any, partly, he thinks, because of the recession and partly because his experience is now a bit out of date. Late last year, he was put on the government's new Work Programme, allocated a slot with the provider Sencia.

"They are supposed to be helping me find work; all they are doing is having me come in and look for jobs on the internet. I could be doing that at home myself. They weren't sending me on any courses," he says. He became rather jaundiced with the system and when his grandmother died in January, he failed to go back. "I missed a few appointments, so my benefits have been sanctioned until December. I wouldn't have done it if I'd known." He has two consecutive six-month sanction periods; most of that time the family gets a hardship payment of £160 a week (a cut of £120 from the £280 they received previously). But for complicated bureaucratic reasons this payment hasn't been made for the past couple of weeks and they have nothing to feed their twin six-year-old sons and their eight-year-old daughter. Sarah is five months pregnant.

Paul doesn't say much, but comments as they wait for the food bank officials to decide whether they are eligible for a fourth, discretionary package that the sanctions system has been very hard for the family. "It cripples you. If it wasn't for the food banks, I don't know how I'd get it, other than steal it. They don't understand what it's going to be like when they take your money away from you, when you've got kids. It's impossible."

"You feel embarrassed coming here," he adds, as a volunteer comes out of the stock room with two plastic bags and a box of food. They say thank you and hurry away, visibly uncomfortable.

Mary Creagh, shadow environment minister, who has responsibility for food and was brought up in Coventry, is ambivalent about the rise in food banks. "There's something about feeling that you are asking for charity rather than getting something from the state … it's humiliating; it involves swallowing your dignity, travelling distances to the centres and walking home with plastic bags," she says.

Volunteers have a much more straightforward attitude. They say they are simply responding to a rise in demand. Graham Carpenter runs the food bank services at the Queens Road Baptist Church. Since the recession began, "we were seeing more people knocking on the door, asking for help", he says. "The jobs that are going around now are half the salary that they were before, or part-time. Coventry used to be a factory town, full of skilled workers, a car factory, a machine town. Now it's a Tesco town. It's just a different city."

In contrast to a soup kitchen, individuals can't just turn up at a food bank and hope to be given supplies. They have to be formally referred and GPs, Jobcentre staff, charities and schools in Coventry issue those they think are in acute need a voucher (printed on red paper so that it can't be easily photocopied) for food that should provide everyone in the recipient's family enough to live on for three days.

In the church hall, food has been divided into categories in big green plastic crates, with labels written in black felt tip on chopped up squares of cardboard – SOUP, BEANS, TOMS, VEG, CUSTARD, RICE PUD, RICE, SUGAR, TEA, JAM, CHOC, SAUCES. All the food comes from donations. When stocks are running low, volunteers stand outside supermarkets and ask shoppers to buy specific items – anything from longlife milk to tins of tuna.

Volunteers have realised it's not a good idea to let recipients into the stockroom. "Then they say: 'Can I have this or that?' It isn't fair to someone who has got nothing to show them £1,000 worth of food, with their eyes lighting up," says Colin Bunting, a volunteer. He and a colleague fill up bags, adhering to a list compiled by the Trussell Trust that is meant to ensure that the handouts are nutritionally sensible.

Inside the storeroom at the Mosaic Church food bank, Hillfields, Coventry. Photograph: Christopher Thomond for the Guardian

There's an eclectic mix of food, some of it of fairly low quality and cheap. Today among the array of goods on offer there is Asda Smart Price chicken-flavour noodles; Tesco Everyday Value chilli con carne; green mung beans in a bag; Sainsbury's Basics chocolate desert mix; a butterscotch supreme desert powder, packed with diglycerides of fatty acids and tetrasodium diphosphate. Staff have a rule that they won't distribute food they wouldn't eat themselves.

"It is a bit annoying when people are clearing out the cupboards and we get rusty tins, something that went out of date in 2011." Bunting says. "We try to be sensitive. We get donations of Weetabix, but the problem with that is that it soaks up a lot of milk. If people give us cream crackers, we wouldn't give them out, because it's insulting if [the recipients] can't afford to buy cheese to eat with it."

The Trussell Trust volunteers check what dietary restrictions people have, and then choose meals for each applicant. "We could give them curry and rice?" Bunting suggests, examining a red voucher.

"Or we could give them pasta with meatballs?" his colleague wonders.

Volunteers say they try not to be critical of the people who come in, but incidental comments show they clearly struggle not to categorise recipients into deserving and undeserving; there is a hint of moralising that might be less pronounced in a state service. There's some uncharitable speculation about why the food bank is less busy in the morning, which goes along the lines of "these people don't get up early". At the Hope Centre there is discussion about how deserving the Romanian families are.

"We try not to be judgmental but if you can't stand close because of the alcohol fumes, you think if you had a couple of bottles less of whisky then maybe you'd be able to buy some food," one of the volunteers says, before catching himself, and adding: "But alcoholism is an addiction. Some people are very grateful and others think it is their right to get food."

There's clearly profound need among the people who arrive to request food. Samantha, who is 22 and living alone with a seven-month-old baby, was made redundant from her job as a nursery nurse when she was 12 weeks pregnant; her maternity payments have ended and she is stuck without money until an application for income support is processed, which could take more than a month.

There's an unemployed chef, 19, who's homeless and living in a Salvation Army hostel, who has tattoos across the side of his head, and is very polite and grateful. "Everyone greets you nicely. Everyone is nice here," he says. "I have never experienced recession before. There are no jobs at the moment."

A 57-year-old who gave up his work to become a carer for his father-in-law who has since died is here because he is finding it hard to get new work. He has been discouraged by recent attempts to apply for jobs. "There was a column to put your date of birth in and it only went back to 1976; with me being born in 1955, I couldn't put my age in so I couldn't apply."

Adrian, 43, who is unemployed, arrives in a wheelchair, unable to walk anywhere because of a blood clot on his leg and back problems, with his girlfriend and carer, Catherine, 28, who used to work as a classroom assistant, but gave it up to be a full-time carer. They are using more public transport to get about, because he is so immobile, which they find soaks up a lot of their money.

"The long and the short of it is, we haven't got any food," he says. "We are both on benefits. We are struggling to keep up with the bills."

Catherine says she had a sandwich with a slice of cheap chicken from Asda, no butter, for her main meal yesterday, and reflects that being hungry "makes you feel sick … tired."

"Dizzy," Adrian adds.

"It can be quite draining," she agrees.

There is no active proselytising, but the food bank recipients sit in the lobby of the church for around 20 minutes waiting for their bags and church staff say that bringing them into the building gets them "curious" and may indirectly encourage attendance.

Gavin Kibble, who runs all the food banks across the city, says that the act of setting up food banks has given a purpose to the church that has been lacking in recent years. The remarkable speed with which food banks have been proliferating across the country is a reflection of need but also of how quickly congregations have recognised that this is something they can do quite easily. "The franchise model of the Trussell Trust is very easy to implement," he says. "The church has lost its relevance and maybe this is a way to find it again."

He used to work as a managing director of a multinational forklift truck company earning a six-figure salary, but wouldn't give up his new role to return to his previous existence because of the "wow factor" of his current job. This appears, in part, to be a sense that divine assistance is being given to ensure that the warehouse is fully stocked.

"There are a lot of wow moments. Food comes just out of the blue when we are stuck. It comes when we need it most and most of the time it is the right stuff." Just as he was worried about the dwindling supplies of sweet treats, manna from heaven arrived in the form of a donation of 999 tins of rice pudding from the Coventry Leofric Lions. He is less enthusiastic about the surplus of baked beans and he mutters: "So many tins of soup and beans. I could sink Coventry with beans."

He has been struck by the number of times when food has arrived just when it is needed. "We believe that there is a provider God who looks after the needs of the food bank. We believe that is the case. The wow moments are spiritual. We can't explain them, so we have to look to something bigger. There are times where coincidence couldn't be coincidence any more."

Not everyone shares this confidence that food will be provided by divine forces. Green says she had noticed that many shoppers were unable to take part in a recent campaign by Sainsbury's to get customers to buy food bank donations with their shopping, saying they couldn't afford to help. Isn't "the idea that we can rely on charity to meet the need bound to be too limited?" she asked during the food bank debate.

The cupboard is bare: food bank recipient Joseph Anderson hasn't worked since 2010. Photograph: Christopher Thomond for the Guardian

Most of the recipients of aid barely notice the religious backdrop to the distribution sessions. Joseph Anderson, 44, is phlegmatic about the whole process. "The reason I am here? The dole decided I missed an appointment so they suspended my money."

He missed the appointment because he didn't have the £3.60 for the bus fare and didn't feel up to the nine-mile walk to the Jobcentre. He hasn't worked since 2010 when he lost his job with ParcelForce, and is anxious to advertise his willingness to do so through the Guardian, hoping there may be readers ready to employ him. He highlights his skills with computer software, but also stresses that he is happy to take any kind of work. "I don't want to be on jobseeker's [allowance]. I'll mend computers or do cleaning – anything. It isn't easy to find work. I'm supposed to turn up smart [to interviews], but that costs money."

He ran out of food six days ago and thinks at home he is down to four tins of baked beans, one tin of ravioli and four potatoes. (Later he reveals the contents of his cupboard, and laughs: "I overestimated – I only had two tins of baked beans.") It is the first time his benefits have been sanctioned and the first time he has received a food voucher. "It's a good service, but we aren't exactly a third-world country. We shouldn't need places like this," he says.